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WAVE AND ELECTROSTATIC COUPLING IN 2-FREQUENCY CAPACITIVELY COUPLED PLASMAS

WAVE AND ELECTROSTATIC COUPLING IN 2-FREQUENCY CAPACITIVELY COUPLED PLASMAS UTILIZING A FULL MAXWELL SOLVER* Yang Yang a) and Mark J. Kushner b) a) Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011, USA yangying@iastate.edu

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WAVE AND ELECTROSTATIC COUPLING IN 2-FREQUENCY CAPACITIVELY COUPLED PLASMAS

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  1. WAVE AND ELECTROSTATIC COUPLING IN 2-FREQUENCY CAPACITIVELY COUPLED PLASMAS UTILIZING A FULL MAXWELL SOLVER* Yang Yanga) and Mark J. Kushnerb) a)Department of Electrical and Computer Engineering Iowa State University, Ames, IA 50011, USA yangying@iastate.edu b)Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, MI 48109, USA mjkush@umich.edu http://uigelz.eecs.umich.edu October 2008 * Work supported by Semiconductor Research Corp., Applied Materials and Tokyo Electron Ltd. YY_MJK_AVS2008_01

  2. University of Michigan Institute for Plasma Science and Engineering AGENDA • Wave effects in 2-frequency capacitively coupled plasma (2f-CCP) sources • Description of the model • Base cases: Ar/CF4 = 90/10, HF = 10-150 MHz • Scaling with: • Fraction of CF4 • HF power • Concluding remarks YY_MJK_AVS2008_02

  3. University of Michigan Institute for Plasma Science and Engineering WAVE EFFECTS IN HF-CCP SOURCES • Wave effects (i.e., propagation, constructive and destructive interference) in CCPs become important with increasing frequency and wafer size. • Wave effects can significantly affect the spatial distribution of power deposition and reactive fluxes. G. A. Hebner et al, Plasma Sources Sci. Technol., 15, 879(2006) YY_MJK_AVS2008_03

  4. University of Michigan Institute for Plasma Science and Engineering GOALS OF THE INVESTIGATION • Relative contributions of wave and electrostatic edge effects determine the plasma distribution. • Plasma uniformity will be a function of frequency, mixture, power… • Results from a computational investigation of coupling of wave and electrostatic effects in two-frequency CCPs will be discussed: • Plasma properties • Radial variation of ion energy and angular distributions (IEADs) onto wafer YY_MJK_AVS2008_04

  5. University of Michigan Institute for Plasma Science and Engineering METHODOLOGY OF THE MAXWELL SOLVER • Full-wave Maxwell solvers are challenging due to coupling between electromagnetic (EM) and sheath forming electrostatic (ES) fields. • EM fields are generated by rf sources and plasma currents while ES fields originate from charges. • We separately solve for EM and ES fields and sum the fields for plasma transport. • Boundary conditions (BCs): • EM field: Determined by rf sources. • ES field: Determined by blocking capacitor (DC bias) or applied DC voltages. YY_MJK_AVS2008_05

  6. University of Michigan Institute for Plasma Science and Engineering FIRST PART: EM SOLUTION • Launch rf fields where power is fed into the reactor. • For cylindrical geometry, TM mode gives Er , Ez and H . • Solve EM fields using FDTD techniques with Crank-Nicholson scheme on a staggered mesh: • Mesh is sub-divided for numerical stability. YY_MJK_AVS2008_06

  7. University of Michigan Institute for Plasma Science and Engineering SECOND PART: ES SOLUTION • Solve Poisson’s equation semi-implicitly: • Boundary conditions on metal: self generated dc bias by plasma or applied dc voltage. • Implementation of this solver: • Specify the location that power is fed into the reactor. • Addressing multiple frequencies in time domain for arbitrary geometry. • First order BCs for artificial or nonreflecting boundaries (i.e., pump ports, dielectric windows). YY_MJK_AVS2008_07

  8. Electron Energy Transport Module Te,S,μ E, N Fluid Kinetics Module Fluid equations (continuity, momentum, energy) Maxwell Equations Plasma Chemistry Monte Carlo Module University of Michigan Institute for Plasma Science and Engineering HYBRID PLASMA EQUIPMENT MODEL (HPEM) • Electron Energy Transport Module: • Electron Monte Carlo Simulation provides EEDs of bulk electrons • Separate MCS used for secondary, sheath accelerated electrons • Fluid Kinetics Module: • Heavy particle and electron continuity, momentum, energy • Maxwell’s Equation • Plasma Chemistry Monte Carlo Module: • IEADs onto wafer YY_MJK_AVS2008_08

  9. University of Michigan Institute for Plasma Science and Engineering REACTOR GEOMETRY • Main species in Ar/CF4 mixture • Ar, Ar*, Ar+ • CF4, CF3, CF2, CF, C2F4, C2F6, F, F2 • CF3+, CF2+, CF+, F+ • e, CF3-, F- • 2D, cylindrically symmetric. • Ar/CF4, 50 mTorr, 400 sccm • Base conditions • Ar/CF4 =90/10 • HF upper electrode: 10-150 MHz, 300 W • LF lower electrode: 10 MHz, 300 W • Specify power, adjust voltage. YY_MJK_AVS2008_09

  10. IEADs INCIDENT ON WAFER: 10/150 MHz Center Edge University of Michigan Institute for Plasma Science and Engineering • IEADs are separately collected over center&edge of wafer. • From center to edge, IEADs downshifted in energy, broadened in angle. • Total Ion • CF3+ • Center • Center • Edge • Edge • Ar/CF4=90/10, 50 mTorr, 400 sccm • HF: 150 MHz/300 W • LF: 10 MHz/300 W YY_MJK_AVS2008_10

  11. IEADs INCIDENT ON WAFER: 10/100 MHz Center Edge University of Michigan Institute for Plasma Science and Engineering • Total Ion • CF3+ • IEADs undergo less change from center to edge than 10/150 MHz. • Center • Center • Edge • Edge • Ar/CF4=90/10, 50 mTorr, 400 sccm • HF: 100 MHz/300 W • LF: 10 MHz/300 W YY_MJK_AVS2008_11

  12. IEADs INCIDENT ON WAFER: 10/10 MHz Center Edge University of Michigan Institute for Plasma Science and Engineering • Less radial change compare to 10/150 MHz case. • Why radial uniformity of IEADs changes with HF ? • Many factors may account for variation: sheath thickness, sheath potential, mixing of ions … • Total Ion • CF3+ • Center • Center • Edge • Edge • Ar/CF4=90/10, 50 mTorr, 400 sccm • HF: 10 MHz/300 W • LF: 10 MHz/300 W YY_MJK_AVS2008_12

  13. ELECTRON DENSITY: Ar/CF4 = 90/10 University of Michigan Institute for Plasma Science and Engineering • HF = 50 MHz, Max = 5.9 x 1010 cm-3 • Changing HF results in different [e] profile, thereby giving different radial distribution of sheath thickness, potential... • [e] profile is determined by wave and electrostatic coupling. • HF = 150 MHz, Max = 1.1 x 1011 cm-3 • HF: 10-150 MHz/300 W • LF: 10 MHz/300 W • Ar/CF4=90/10 • 50 mTorr, 400 sccm YY_MJK_AVS2008_13

  14. University of Michigan Institute for Plasma Science and Engineering AXIAL EM FIELD IN HF SHEATH • HF = 50 MHz, Max = 410 V/cm • Ar/CF4=90/10, 50 mTorr, 400 sccm • HF: 10-150 MHz/300 W • LF: 10 MHz/300 W • HF = 150 MHz, Max = 355 V/cm • |Ezm| = Magnitude of axial EM field’s first harmonic at HF. • No electrostatic component in Ezm: purely electromagnetic. • 150 MHz: center peaked due to constructive interference of plasma shortened wavelengths. • 50 MHz: Small edge peak. YY_MJK_AVS2008_14

  15. University of Michigan Institute for Plasma Science and Engineering AXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz • ANIMATION SLIDE-GIF • |EZ| in HF (150 MHz) Sheath, Max = 1500 V/cm • |EZ| in LF(10 MHz) Sheath, Max = 1700 V/cm • Significant change of |Ez| across HF sheath as evidence of traveling wave. • HF source also modulates E-field in LF sheath. • Ar/CF4=90/10 • 50 mTorr, 400 sccm • HF: 150 MHz/300 W • LF: 10 MHz/300 W YY_MJK_AVS2008_15a

  16. University of Michigan Institute for Plasma Science and Engineering LF CYCLE AVERAGED AXIAL E-FIELD IN HF AND LF SHEATH: 10/150 MHz • |EZ| in HF (150 MHz) Sheath, Max = 450 V/cm • |EZ| in LF(10 MHz) Sheath, Max = 750 V/cm • Significant change of |Ez| across HF sheath as evidence of constructive interference. • Ar/CF4=90/10 • 50 mTorr, 400 sccm • HF: 150 MHz/300 W • LF: 10 MHz/300 W YY_MJK_AVS2008_15b

  17. SPATIAL DISTRIBUTION OF NEGATIVE IONS University of Michigan Institute for Plasma Science and Engineering • [CF3-+ F-] • HF = 150 MHz, Max = 1.2 x 1011 cm-3 • Finite wavelength effect at 150 MHz populates energetic electrons in the reactor center. • More favorable to attachment processes (threshold energies  3 eV) than ionization (threshold energies  11 eV). • [CF3- + F-] increases in the center. • HF: 10-150 MHz/300 W • LF: 10 MHz/300 W • Ar/CF4=90/10 • 50 mTorr, 400 sccm YY_MJK_AVS2008_16

  18. SPATIAL DISTRIBUTION OF POSITIVE IONS • Ar+ • CF3+ • Difference in radial profiles for different ions. • Different sheath transiting time due to differences in mass and sheath thickness. • Eventually translates to radial non-uniformity of IEADs. • HF: 10-150 MHz/300 W • LF: 10 MHz/300 W • Ar/CF4=90/10 • 50 mTorr, 400 sccm University of Michigan Optical and Discharge Physics YY_MJK_AVS2008_17

  19. ELECTRON IMPACT IONIZATION SOURCE FUNCTION • HF = 10 MHz, Max = 2.1 x 1015 cm-3s-1 • Source from bulk and secondary electrons. •  50 MHz: bulk ionization from Ohmic heating, edge peaked due to electrostatic field enhancement.. • 150 MHz: ionization dominated by sheath accelerated electrons (stochastic heating). • 100 MHz: has both features, but edge effect dominates. • HF = 50 MHz, Max = 6.3 x 1015 cm-3s-1 • HF = 100 MHz, Max = 4.2 x 1015 cm-3s-1 • HF = 150 MHz, Max = 3.8 x 1016 cm-3s-1 • HF: 10-150 MHz/300 W • LF: 10 MHz/300 W • Ar/CF4=90/10 • 50 mTorr, 400 sccm University of Michigan Optical and Discharge Physics YY_MJK_AVS2008_18

  20. ION FLUXES INCIDENT ON WAFER University of Michigan Institute for Plasma Science and Engineering • Total Ion Flux • CF3+ Flux • Uniformity of incident ion fluxes and their IEADs are both determined by plasma spatial distribution. • Relative uniform fluxes and IEADs at 100 MHz. • HF: 10-150 MHz/300 W • LF: 10 MHz/300 W • Ar/CF4=90/10 • 50 mTorr, 400 sccm YY_MJK_AVS2008_19

  21. IEADs INCIDENT ON WAFER: Ar/CF4 = 80/20 University of Michigan Institute for Plasma Science and Engineering Center Edge • Less radial variation across the wafer. • More radial uniformity of sheath thickness and potential counts. • Implicates adding CF4 improves plasma uniformity. • Total Ion • CF3+ • Inner • Inner • Outer • Outer • Ar/CF4=80/20, 50 mTorr, 400 sccm • HF: 150 MHz/300 W • LF: 10 MHz/300 W YY_MJK_AVS2008_20

  22. University of Michigan Institute for Plasma Science and Engineering SCALING WITH FRACTION OF CF4 IN Ar/CF4: 10/150 MHz • Pure Ar, Max = 3.8 x 1011 cm-3 • With increasing fraction of CF4: • [e] decreases thereby decreasing conductivity. • Weakens constructive interference of EM fields by increasing wavelength. • Maximum of [e] shifts towards the HF electrode edge. • Skin depth also increases. • Increasing penetration of EM fields. • More uniform [e] profile results. • 10% CF4, Max = 1.1 x 1011 cm-3 • 20% CF4, Max = 4.8 x 1010 cm-3 • 30% CF4, Max = 4.4 x 1010 cm-3 • HF: 150 MHz/300 W • LF: 10 MHz/300 W • 50 mTorr, 400 sccm YY_MJK_AVS2008_21

  23. ION FLUXES INCIDENT ON WAFER: 10/150 MHz University of Michigan Institute for Plasma Science and Engineering • Total Ion Flux • CF3+ Flux • Uniform [e] profile at 20% CF4 results in • Radial uniformity of incident ion fluxes. • Uniform radial profile of IEADs. • HF: 150 MHz/300 W • LF: 10 MHz/300 W • 50 mTorr, 400 sccm YY_MJK_AVS2008_22

  24. SCALING TO HF POWER: 10/150 MHz University of Michigan Institute for Plasma Science and Engineering • [e] • 1000 W, [CF3-+ F-] • Increasing HF power reduces plasma uniformity. • Finite wavelength effect preferentially produces negative ions in the center. • With increasing [e], wave penetration is less affected in the radial direction due to the HF sheath, so [e] peak only moves 2 cm from 300 W to 1000 W. • HF: 50-150 MHz • LF: 10 MHz/300 W • Ar/CF4=90/10 • 50 mTorr, 400 sccm YY_MJK_AVS2008_23

  25. IMPACT OF HF POWER ON ION FLUXES ONTO WAFER University of Michigan Institute for Plasma Science and Engineering • Total Ions Flux • Non-uniformity of ion fluxes onto the wafer also increases with increasing HF power. • HF: 50-150 MHz • LF: 10 MHz/300 W • Ar/CF4=90/10 • 50 mTorr, 400 sccm YY_MJK_AVS2008_24

  26. TOTAL ION IEADs INCIDENT ON WAFER Center Edge • More uniform IEADs at higher HF power. • With increasing HF power (increasing [e]), LF voltage decreases to keep LF power constant. • Diminishes radial variation of IEADs. • 300 W • 1000 W • Center • Center • Edge • Outer • Ar/CF4=90/10, 50 mTorr, 400 sccm • HF: 150 MHz • LF: 10 MHz/300 W University of Michigan Optical and Discharge Physics YY_MJK_GEC2008_25

  27. CONCLUDING REMARKS University of Michigan Institute for Plasma Science and Engineering • A full Maxwell solver separately solving for EM and ES fields was developed and incorporated into the HPEM. • For 2f-CCPs sustained in Ar/CF4=90/10 mixture, • HF determines wave and electrostatic coupling which, in turn, determines plasma spatial distribution. • Non-uniform IEADs across the wafer at HF =150 MHz due to plasma non-uniformity. • Increasing fraction of CF4 to 20% results in more uniform plasma profile and IEADs incident on wafer. • At HF = 150 MHz, increasing HF power increases plasma non-uniformity. YY_MJK_AVS2008_26

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